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Apr 8, 2016 at 13:23 comment added Serguei Popov Essentially, Chapter 5 covers both discrete and continuous cases. For example, Theorem 5.3.1 is formulated in the continuous case, but (as noted there in the text) the results in the discrete case are the same. Up to Section 5.2, the results are general (the chain lives on a set $\Sigma$, which can be $\mathbb{R}$ or $\mathbb{Z}$).
Apr 8, 2016 at 5:59 comment added Lotayou Thank you for your prompt answer. However I was more concerned in the case where ${\sigma_{n}}$ are discrete. What's the corresponding result under this assumption?
Apr 7, 2016 at 14:48 history answered Serguei Popov CC BY-SA 3.0